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UKMT Intermediate Mathematical Challenge, 2023

Algebra Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

The numbers $x$ and $y$ satisfy both of the equations $23x + 977y = 2023$ and $977x + 23y = 2977$ . What is the value of $x^2 - y^2$ ?

(A) $1$ (B) $2$ (C) $3$ (D) $4$ (E) $5$

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